Question

13 cos A = 5, then tan A is cbse class10​

Answer 1

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13 cos A = 5, then find tan A

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$\tt{as \: we \: know} \: \mathbb{ \blue{ cos \: a \: = \frac{base}{hyp.} }}$

$\tt{ \to13 \: cos \: a = 5}$

${ \to \: cos \: a = \frac{5}{13} }$

$\tt{ \color{green}{\therefore \: base = 5 \: \: \: \: hyp. = 13}}$

$\tt{ \color{gold}{using \: ac {}^{2} = ab {}^{2} + bc {}^{2} }}$

$\tt{\to13 {}^{2} = 5 {}^{2} + bc {}^{2} }$

$\tt{ \to \: bc {}^{2} = 169 - 25}$

$\tt{ \to \: bc = \sqrt{144} }$

$\tt{ \to \: bc = 12}$

$\tt \color{green}{\therefore \: height = 12}$

$\tt \blue{tan\: a = \frac{height}{base} }$

$\tt{tan \: a = \frac{12}{5} }$

ㅤ

$\tt \red{\huge{ \therefore \: tan \: a= \frac{12}{5}} }$